Second-Order Homogeneous ODEs: Complex Characteristic Roots (Differential Equations)
Free printable university Differential Equations worksheet on second-order ODEs whose characteristic equation has complex conjugate roots, writing the real general solution with sines and cosines.
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Differential Equations · Math worksheet
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Second-Order Homogeneous ODEs: Complex Characteristic Roots
Each characteristic equation has complex conjugate roots a ± bi. Write the real general solution y = e^(ax)(C₁cos(bx) + C₂sin(bx)).
- 1.y″ + y = 0
- 2.y″ + 4y = 0
- 3.y″ + 9y = 0
- 4.y″ + 16y = 0
- 5.y″ + 4y′ + 8y = 0
- 6.y″ + 6y′ + 25y = 0
- 7.y″ + 6y′ + 13y = 0
- 8.y″ + 4y′ + 13y = 0
- 9.y″ + 2y′ + 17y = 0
- 10.y″ + 6y′ + 18y = 0
- 11.y″ + 2y′ + 10y = 0
- 12.y″ + 6y′ + 10y = 0
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